The electromagnetic backscattering of a crosscut of a cruise missile coated by a thin homogeneous layer made of radar absorbent material is modeled using a finite element method. Based on the radar cross section and a reflection coefficient, optimization problems are formulated for evaders and interrogators leading to optimal material parameters for the coating and optimal monostatic radar operating frequencies, respectively. Optimal coating materials are constructed for several radar frequencies. Tuning only dielectric permittivity gives a narrow frequency range of high absorption while also tuning magnetic permeability widens it significantly. However the coating layers considered do not provide substantial reduction of backscattering in the entire frequency range from 0.2 to 1.6 GHz. Computational experiments also demonstrate that the reflection coefficient based on a simple planar geometry can predict well the strength of radar cross section in the sector of interest with a substantially reduced computational burden.